System and method for propagating information using modified nucleic acids

ABSTRACT

A method is provided for improving a nucleic acid-based molecular computing system comprised of (i) a nucleic acid structure, (ii) at least one polynucleotide displacement molecule that can bind with the nucleic acid structure under hybridizing conditions, and (iii) a clashing polynucleotide molecule that competes with the polynucleotide displacement molecule for binding the nucleic acid structure under the hybridizing conditions The method entails incorporation of chemical modification that inhibits the binding of the clashing molecule and the nucleic acid structure or facilitates the binding of the displacement molecule and the nucleic structure.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application claims priority to U.S. provisional application No.61/349,012, filed May 27, 2010, the entire contents of which areincorporated herein by reference.

BACKGROUND OF THE INVENTION

Nano-scale computers can potentially be realized using molecules. Suchcomputers may be suited for solving certain computation problems. Inparticular, computers employing biomolecules can be compatible withbiological environments, and can potentially be used for complex diseasediagnostics or even treatments.

The ability to translate one nucleic acid sequence into another can beemployed to build logic gates and networks with nucleic acids. Thesegates and networks are driven by two events: hybridization and stranddisplacement. Both events are generally thermodynamically favorable;that is, they involve a transition from a higher to a lower-energystate. Thus, both events can occur spontaneously in a system.

Hybridization involves free, single-stranded stretches of nucleic acids.Accordingly, a nucleic-acid network may be regulated by the availabilityof these free strands.

A “sequestering event” allows certain sequences to be availableconditionally to the rest of the network. Such events empower theconstruction of translators, which convert one single-stranded nucleicacid sequence into a different single-stranded nucleic acid sequence.These translators are the foundation on which basic logic operators,such as AND, NOT, OR, NAND, NOR, XOR and XNOR, can be built with nucleicacids. From these and other logic components, larger networks can beconstructed that include components such as amplifiers. As a result,these translation events are important for information processing withnucleic acids and molecular computing.

SUMMARY OF THE INVENTION

In accordance with one aspect of the present invention, a method isprovided for improving a nucleic acid-based molecular computing system.The method includes: (A) identifying a computing system comprised of (i)a nucleic acid structure that includes an incompletely base-pairedduplex domain, (ii) at least one polynucleotide displacement moleculethat can bind with the nucleic acid structure under hybridizingconditions, such that the nucleic acid structure undergoes a transitionin energy state due to a branch migration reaction involving the duplexdomain, and (iii) a clashing polynucleotide molecule that competes withthe polynucleotide displacement molecule for binding the nucleic acidstructure under the hybridizing conditions but that cannot produce abranch migration reaction involving the duplex domain; then (B)reconfiguring at least one of the displacement molecule and the nucleicacid structure, respectively, to incorporate a chemical modificationrelative to a first reference molecule that comprises naturalnucleosides and has the same sequence content as the displacementmolecule or the nucleic acid structure, as the case may be. Theaforementioned the modification causes binding of the displacementmolecule and the nucleic acid structure to have a hybridization freeenergy, differing from that of a first reference binding between thedisplacement molecule or the nucleic acid structure and the firstreference molecule, such that the branch migration reaction isfacilitated relative to the first reference binding. After or in placeof step (B) is a step (C) of reconfiguring at least one of the clashingmolecule and the nucleic acid structure, respectively, to incorporate achemical modification relative to a second reference molecule thatcomprises natural nucleosides and has the same sequence content as theclashing molecule or the nucleic acid structure, as the case may be. Themodification causes binding of the clashing molecule and the nucleicacid structure to have a hybridization free energy, differing from thatof a second reference binding between the clashing molecule or thenucleic acid structure and the second reference molecule, such thatbinding of the clashing molecule is impeded relative to the secondreference binding.

The invention also provides, in another of its aspects, a system thatincludes (A) a nucleic acid structure that comprises an incompletelybase-paired duplex domain; (B) at least one polynucleotide displacementmolecule to effect binding with the nucleic acid structure underhybridizing conditions, such that the nucleic acid structure undergoes atransition in energy state due to a branch migration reaction involvingthe duplex domain; and (C) at least one polynucleotide clashing moleculecapable of binding with the nucleic acid structure under hybridizingconditions, such that the nucleic acid structure and the clashingmolecule are bound and prevent the binding of the polynucleotidedisplacement molecule. At least one of the displacement molecule and thenucleic acid structure, respectively, has a chemical modificationrelative to a reference molecule that comprises natural nucleosides andhas the same sequence content as the displacement molecule or thenucleic acid structure, as the case may be. The modification causes thebinding to have a hybridization free energy, differing from that of areference binding between the displacement molecule or the nucleic acidstructure and a reference molecule, such that the branch migrationreaction is facilitated relative to the reference binding. In additionor in the alternative, at least one of the clashing molecule and thenucleic acid structure, respectively, has a chemical modificationrelative to a reference molecule that comprises natural nucleosides andhas the same sequence content as the displacement molecule or thenucleic acid structure, as the case may be. The modification causes thebinding to have a hybridization free energy, differing from that of areference binding between the displacement molecule or the nucleic acidstructure and a reference molecule, such that binding of the clashingmolecule is impeded relative to the reference binding.

In yet another aspect, a system is provided for propagating information.The system includes a first molecule and a second molecule configured tobind with the first molecule. At least one of the first molecule and thesecond molecule, respectively, has a chemical modification relative to areference molecule that has the same sequence content as the firstmolecule or the second molecule, as the case may be. The modificationcauses the binding to have a free energy different from that of areference binding between the reference molecule and the first or secondmolecule, such that at least one of the following is realized in thesystem: a probability of a productive binding is raised, or aprobability of an unproductive binding is reduced.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates a solid-phase sequestering implementation of anucleic acid translator, where individual section (A, B, etc) representstretches of oligonucleotides of arbitrary length and sequence.

FIG. 1B illustrates how a solid-phase sequestering implementation of anucleic acid translator sequesters stretches of oligonucleotides.

FIG. 2A illustrates a “toe-hold” sequestering implementation of anucleic acid translator. Again, individual sections represent stretchesof oligonucleotides of arbitrary length and sequence.

FIG. 2B illustrates how a “toe-hold”-sequestered implementation of anucleic acid translator sequesters stretches of oligonucleotides.

FIG. 3A shows a system of three toe-hold sequestered nucleic acidtranslators. The reactions shown are all strand-displacement reactionsthat proceed by the same branch-migration mechanism as in FIG. 2A.

FIG. 3B shows a system with the same oligonucleotides as are shown inFIG. 3A but, instead of strand displacement reactions, toe-hold“clashes” are shown, where the toe-hold is bound by a sequence thatcannot produce a strand displacement reaction. This binding eventoccupies the toe-hold such that the desired strand cannot bind.

FIG. 3C illustrates different architectures for incompletely base-pairednucleic acid structures including: (a) terminal; (b) internal loop; and(c) and (d) multi-part complex.

FIG. 4 presents a schematic depiction of how, in the system of nucleicacid translators shown in FIG. 3A, the equilibrium can be shifted tofavor strand displacement reactions over toe-hold clashes by replacingthe stretches of oligonucleotides with chemical modifications thatincrease the binding affinity and/or the stretches of oligonucleotideswith modifications that decrease the binding affinity.

FIG. 5 shows modified backbone structures for nucleic acid analogs,where “B” represents an arbitrary nucelobase, and (a) shows a naturalphosphodiester backbone found in DNA, (b) shows peptide nucleic acids,(c) shows guanidinium peptide nucleic acids, (d) shows L-serine derivedgamma-PNAs, and (e) shows phosphorodiamidates (here with a morpholinosugar).

FIG. 6 illustrates modified sugar structures for nucleic acid analogs,where “B” represents an arbitrary nucleobase, and (a) shows a naturaldeoxyribose sugar found in DNA, (b) shows morpholinos, (c) shows lockednucleic acids, and (d) shows fluorine-modified RNA derivative.

FIG. 7 illustrates modified nucelobase structures for the nucleic acidanalogs methylcytosine (a), diaminopurine (b), phenoxazine (c), andG-clamp (d).

FIG. 8 illustrates a fluorescence kinetics assay for indicating thereaction rate change due to a chemical modification according to theinvention.

DETAILED DESCRIPTION

Various approaches, such as solid-phase sequestering, toe-holdsequestering, and toe-hold exchange, can be used in translating nucleicacid sequences to build logic operators and networks. These threeparticular approaches, described in greater detail below, areexemplified via geometries that utilize three-way, toe-hold-mediatedbranch migration reactions. Additional mechanisms are possible forbranch migration reactions, however, including but not limited tofour-way branch migration, four-way accelerated migration, andmulti-strand complex migration.

Thus, while the following embodiments are described using three-waybranch migration for illustration purposes, the present inventioncontemplates DNA logic gates and networks built to utilize other branchmigration pathways. Conversely, the embodiments of the invention can beapplied to any branch migration reaction.

Solid-phase sequestering uses physically separating the relevantsequences/strands in space, using beads, nanoparticles, or surfaces todo so. This approach employs principles of site isolation, which hasbeen used extensively in the organic chemistry context. In solid-phasesequestered geometries, when these displacement events occur can becontrolled by regulating whether the necessary strands are in thesolution or in the solid phase of the system.

FIG. 1A shows a basic solid-phase sequestering setup for a translator—acomponent that allows a system to substitute one nucleic acid sequencefor another. Here, the strand A′-X′ (where A and X each represent astretch of oligonucleotides of arbitrary length and sequence and X′ andA′ represent their respective reverse complements) is bound to a solidsupport and is initially hybridized to Y-B-X, forming a nucleic acidstructure in the form of an incompletely base-paired duplex, which canfunction as a translator. In this configuration, the strand Y-B-X issolid-phase sequestered and cannot interact with the rest of the system.However, in the presence of the strand X-A, referred to as a“polynucleotide displacement molecule,” strand Y-B-X can be displacedfrom the solid support and exposed to the solution phase of the system,while strand X-A is bound to the support. This operation involves twosteps, the first of which is the hybridization of complementarysequences A and A′ (often referred to as toe-hold binding). In thesecond step, the X region of strand X-A binds to the X′ region of A′-X′,displacing the X region of Y-B-X and releasing this strand into solutionwhile leaving X-A bound to the solid support (this step is oftenreferred to as a branch migration reaction). This two-step processeffectively allows for the translation of a free X-A strand into a freeY-B-X strand.

FIG. 1B shows a system having an input strand X-A interacting with anincompletely base-paired duplex, “Translator 1.” The output includes acompletely base-paired duplex, A′-X′/X-A, which is considered a “waste”product, and an output strand Y-B-X, which is referred to as “Output 1”and can be used as “Input 2” in a further reaction. “Input 2” interactswith “Translator 2” and produces the “Output 2” and another wasteproduct. In this figure, the B region of strand Y-B-X illustrates thesequestering of sequences in this network. At the start, Y-B-X cannothybridize with the B′ region of Translator 2 because both are isolatedon separate solid-supports. When Input 1 binds to Translator 1 andreleases Y-B-X into solution, Y-B-X can then interact with Translator 2.Therefore, the ability of Y-B-X and Translator 2 to interact isconditional on the presence of Input 1.

The strands bound to one solid surface interact extremely slowly withstrands on another solid surface due to steric effects. Consequently,the strands in the solution phase are the only components that caninteract with the solid phase operators.

Toe-hold sequestering and toe-hold exchange are separate approaches thatuse similar pairing interactions, but with different geometries. Bothcan accomplish the same operations as solid-phase translators, butfunction by keeping stretches of sequence bound up in a duplex. Just asin the solid-phase translator, a displacement event can free thesequence of interest. For both toe-hold geometries, all of the strandscan be in solution together, by the consequence of which displacementevents are regulated by the availability of toe-holds, i.e., shortstretches of single-strand nucleic acid sequences that provide astarting point for a displacement event.

FIG. 2A shows a toe-hold sequestered translator similar to the one inFIG. 1A, but based on toe-hold rather than solid-phase sequestering. Inthis example, the A′ region of the translator is the toe-hold that bindsthe input strand and allows the strand displacement reaction to proceed.

FIG. 2B shows a toe-hold-based system having an input strand A-X-Binteracting with an incompletely base-paired duplex, “Translator 1.” Theoutput includes a waste product, i.e., a completely base-paired duplex,B′-X′-A′/A-X-B, and “Output 1” strand X-B-Y-C, which can be used as“Input 2” in a further reaction. “Input 2” interacts with “Translator 2”and produces the “Output 2” and another waste product. In this figure,the B region of X-B-Y-C is sequestered in Translator 1 by beinghybridized to a complementary B′ region and therefore unable to interactwith the B′ region of Translator 2. The ability of X-B-Y-C to interactwith Translator 2 is conditional on the presence of Input 1 (A-X-B) inthe system.

The toe-hold geometries have the potential to be very useful, but theiruse to date has been limited by the rate at which a system containingsuch toe-hold geometries can propagate information. This is due toinherent limitations, present in the current toe-hold sequesteredapproaches, which slow them down below a biologically useful timescale.These kinetic bottlenecks are a result of unproductive reactions,referred to here as “toe-hold clashes,” that occur when a toe-hold isbound by a molecule having a complementary sequence or “clashing strand”that cannot produce a displacement reaction.

FIG. 3A shows a system of three toe-hold sequestered nucleic acidtranslators, much like the one in FIG. 2A. If all three strands are insolution together, however, there are other binding events that can takeplace. FIG. 3B illustrates some of the non-productive binding events orclashes that can take place. By involving a “polynucleotide clashingmolecule,” these events do not lead to a displacement reaction but canslow the system down, because the incidence of a clashing strand blocksstrands from binding that can produce a displacement reaction.

Toe-holds can be kept short to mitigate the effect of these clashes onthe system: the shorter the toe-hold is, the faster the on/off rate ofthe complementary sequence can be. Thus, five or six nucleotide-longtoe-holds are common because at these lengths, if a non-productivebinding event occurs, the time spent in the double-stranded, “clashed”state is short. This approach creates the aforementioned kineticbottleneck, however, because the productive binding event is constrainedby the same thermodynamic parameters; hence, the incoming strandlikewise does not bind strongly to these toe-holds. Consequently, thedesired displacement does not always occur when the correct incomingstrand binds, as it needs to be in the bound state long enough toinitiate the displacement reaction. The use of short toe-holds thusincreases the amount of time required for a given operation to occur andproduce an output. Put another way, the displacement reaction cannottake place before the occurrence of many binding events, both byclashing strands and by desired strands. This inefficiency limits theutility of the system by slowing down the propagation of information totime scales that are too extended to be useful.

Pursuant to one aspect of the invention, by virtue of chemicalmodification of the nucleic acid structure and/or the polynucleotidedisplacement molecule, the productive interactions are facilitated. Thismakes it feasible for chaining individual logic gates together intonetworks of arbitrary size for biological applications. Morespecifically, an approach is provided to determine how to disfavorclashing interactions and favor productive interactions without alteringthe information content of the sequences.

In accordance with the invention, these approaches improve thethermodynamics of binding for the desired strand and/or disfavor thethermodynamics for the clashing strands, all without altering thesequence content. In particular, using chemically-modified structures,the Gibbs free energy (ΔG) for the desired hybridization reactionbetween a given oligonucleotide and its DNA or RNA complement is reducedand/or the ΔG of the clashing interaction is increased. On a molecularlevel, these respectively correspond to a tighter binding (higherbinding affinity) of desired hybridization reaction and to a less tightbinding (lower binding affinity) for clashing strands, resulting fromthe modification of the structures.

The former shifts the equilibrium for desired binding events with thetoe-hold toward the duplex (bound) state, creating a better chance forthe displacement reaction to occur without affecting the equilibrium ofbinding between the toe-hold and clashing strands. The latter disfavorsthe binding of the clashing strand(s), making these interactions favorthe unbound state. These two changes can be used separately or together,in order to favor the binding of the desired strand and disfavor thebinding of the clashing strand(s).

Embodiments in accordance with the invention take advantage of the factthat the reaction rate of any toe-hold mediated strand displacement isrelated to the thermodynamic favorability of the two nucleic acidstrands or complexes being bound. By making these thermodynamics morefavorable for the non-clashing binding events and/or less favorable forclashing binding events, one can drive the system toward productivedisplacement reactions. This will speed up the rate at which informationis propagated to the point that it can be used on biologically relevanttimescales. The approach of the invention, described here, accomplishesthis through chemical modifications to stretches of oligonucleotides inthe system.

By virtue of such chemical modification of the nucleic acid structureand/or of the polynucleotide molecule, pursuant to invention, theeffective concentration range is widened over which the reaction isoptimal. This happens because the percentage of nucleic acid in a duplexat a given temperature is a function of concentration and of the ΔG ofthe hybridization reaction. Thus, the more concentrated a set ofcomplementary oligonucleotides is, the higher the percentage of duplexformation and the lower (more favorable) the AG is, the higher thepercentage of duplex formation. Changing the ΔG for a given interactiontherefore changes the percent duplex at a given concentration. Loweringthe ΔG (i.e., making the interaction more favorable) means that therewill be a higher percentage of duplex at a given concentration, whileraising the ΔG (making the interaction less favorable) means there willbe a lower percentage of duplex at the same concentration. This effectwidens the optimal concentration range at which these reactions can bepractically used, as desired duplexes can be formed at lowerconcentrations and undesired duplexes will not be formed at higherconcentrations, relative to a reference set of unmodifiedoligonucleotides.

These approaches apply to any toe-hold-mediated reaction geometry,including but not limited to the 3-way branch migration reactionsdiscussed above. Different architectures can be used for theincompletely base-paired duplex where branching or loops are located atdifferent points in the structure (see FIG. 3C, for instance). Theorientation of the branches or loops is not predicated on thedirectionality of the strand. Thus, these structures can include (a) aterminal structure, (b) an internal loop, or (c) and (d) a multi-partcomplex, or any other possible architectures for an incompletelybase-paired duplex.

These nucleic acid structures can translate an active “input” sequence(the displacement polynucleotide) into an active “output” sequence (thepolynucleotide which is released).

The nucleic acid structures called “translators” above can be at theirrespective thermodynamic minimum; i.e., they are the most stablestructures that the particular set of nucleic acid sequences can form.These structures can be formed by annealing the two or more individualnucleic acid strands. For instance, all of the strands can be mixedtogether, heated to well above the melting point for any structure toform, and then slowly cooled down. This allows the strands to hybridizein the lowest possible energy state (thermodynamic minimum).

This procedure can be the same for natural nucleic acids like DNA andRNA, nucleic acids with modified backbones, sugars, or bases, and forchimeras made up of natural and modified nucleic acids.

Selective incorporation of specific chemical modifications can favor thebinding of strands capable of productive displacement reactions overtoe-hold clash binding events. For example, FIG. 4 shows the samestrands as FIGS. 3A and 3B. However, if certain stretches of nucleicacids are replaced with chemically modified analogs that improve thethermodynamics of binding, the kinetics for clashes shifts in favor ofthe displacement reactions. For example, if the “B” stretch ofoligonucleotides in the strand X-B-Y-C (circled with a solid line) has ahigher binding affinity for B′ than the “B” stretch of oligonucleotidesin the strand A-X-B, the equilibrium shifts in favor of the productive,strand displacement reaction, which increases the probability orfrequency with which this reaction occurs. Both B′s have the sameWatson-Crick base pairing sequence, but the interaction between X-B-Y-Cand the B′ toe-hold is more favorable due to chemical modifications.

Similarly, if certain stretches of nucleic acids are replaced withanalogs that disfavor binding, the equilibrium will shift away from theclashes as well. For instance, if “B” in the strand A-X-B (circled witha dashed line) has a lower binding for B′ than “B” in X-B-Y-C, then theequilibrium will shift away from the toe-hold clash, improving thekinetics for a strand displacement reaction.

Both approaches accelerate the speed at which a nucleic acid network canprocess signals because both increase the residence time of the desiredstrand on the toe-hold relative to the residence time of the clashingstrand or strands. This provides a better chance that the stranddisplacement reaction will occur in a given period of time and thusincreases the rate at which the network evaluates a given input or setof inputs. These modifications have not previously been used tofacilitate or disfavor displacement reactions, to build significant DNAlogic gates and networks, or to propagate information.

There are many well-characterized nucleic acid modifications that can beused in accordance with embodiments of the invention to improve orreduce the thermodynamic properties of binding to natural DNA or RNA.These include changes to the backbone, sugar, or nucleobase of theoligonucleotide. These modifications also can be used separately or inconjunction with one another; that is, using a modified backbone doesnot preclude the use of a modified nucleobase in the same strand.

Nucleic acid backbone analogs can be used to improve the binding ofstrands capable of producing a displacement reaction. There are a numberof different analogs that could be used, all of which offer tighterbinding affinities to DNA and RNA than natural nucleic acids. Theseanalogs include but are not limited to those with uncharged backbones(peptide nucleic acids or phosphorodiamidates), positively chargedbackbones (guanidinium peptide nucleic acids), and hydrogen-bondinggroups that allow for pre-organization (gamma peptide nucleic acids).

The general structures for certain analogs are shown in FIG. 5. Theseanalogs all improve the thermodynamics of nucleic acid hybridizationreactions, allowing for tighter toe-hold binding and therefore fasterdisplacement. By using these analogs in specific places of the logicnetwork, the desired displacement reactions can be strongly favored incomparison to the clashing interactions, thus accelerating the rate ofinformation processing.

The use of modified sugar rings can also alter the thermodynamics ofbinding to DNA or RNA for an oligonucleotide. The most widely usedanalogs are morpholinos, locked nucleic acids (LNAs), and LNAderivatives. Other modified sugars are documented in the literature thatalso could produce a similar result, in terms of altering bindingthermodynamics. Illustrative of these are sugars with modifications atthe 1′, 2′, 3′ or 4′ position and sugars with different atomssubstituted for the oxygen in the ribose cyclopentane ring. Theseanalogs are illustrated in FIG. 6.

Nucleobase modifications can also be used to achieve the same effect asbackbone and sugar analogs; namely, altering the thermodynamics ofspecific hybridization reactions. These bases include methylcytosine,diaminopurine, G-clamp, and phenoxazine (FIG. 7), all of which improvethe binding affinity of a strand for its reverse complement. Anotheropportunity that exists with nucleobase modification involvespseudocomplementary bases. This class of base analogs forms weak basepairs with one another but forms strong base pairs with standard bases.One such pair of bases is 2-aminoadenine (nA) and 2-thiothymine (sT).These bases could be used to favor one strand binding while disfavoringanother, an example of increasing the likelihood of a productive bindingevent while decreasing the likelihood of a clash at the same time.

Another chemical modification that could be used to alter thethermodynamics of binding interactions is the incorporation of chargedpolymers like chitosan, which has been shown in the literature toaccelerate the rate of displacement reactions. However, since thesepolymers speed up reactions non-specifically, they would have to be usedin conjugation with one of the other modifications mentioned above toallow for discrimination between desired and undesired binding events.

Different approaches can be used to synthesize the molecules with thechemical modifications discussed above. For example, the backbonechemistry can be taken into consideration of the design of the modifiedmolecules. Backbone chemistry is what is used to put together individualmonomers into a longer strand. Modifications that involve the nucleobaseor the sugar but that keep the natural phosphodiester backbone ofDNA/RNA can be synthesized via standard phosphoramidite chemistry, asemployed for natural monomers. Illustrations of these methods are found,for example, in Beaucage, S., and R. Iyer, Tetrahedron 48: 2223 (1992),in Brown, D. M. A, “Brief history of oligonucleotide synthesis,” 20METHODS IN MOLECULAR BIOLOGY (Protocols for Oligonucleotides andAnalogs) 1-17 (1993), in Reese, Colin B., Organic & BiomolecularChemistry 3: 3851 (2005), and in Iyer, R. P.; and S. L. Beaucage, “7.05.Oligonucleotide synthesis,” 7 COMPREHENSIVE NATURAL PRODUCTS CHEMISTRY(DNA and Aspects of Molecular Biology) 105-52 (1999), the respectivecontents of which are hereby incorporated by reference in theirentirety.

If the backbone is being changed in a particular modification, differentchemistry will be employed. Such modification chemistry is generallyknown in the scientific literature. Thus, peptide nucleic acids (PNAs)and their derivatives rely on amide bonds to link the individualmonomers together. Instead of using phosphoramidite chemistry,therefore, strands of these monomers are made with amide bonding formingconditions and coupling reagents like HBTU. An exploration of themethods used to make PNA or PNA-like oligonucleotides can be found, forinstance, in F. Beck, “Solid Phase Synthesis of PNA Oligomers,” METHODSIN MOLECULAR BIOLOGY SERIES (Peptide Nucleic Acids), Humana Press,http://www.springerlink.com/content/mr571738x7t65067/.

Another backbone modification approach involves chimericoligonucleotides. These are oligonucleotide strands that containdifferent backbone chemistries in the same molecule. For example, if oneneeded a strand that was half PNA backbone and half DNA backbone, onewould need a way to join these two different backbone chemistries.Making these chimeric strands is also generally known in the art. In theabove example of a PNA/DNA chimera, the difference in chemistries can bebridged by using modified DNA or PNA monomers. For DNA, the5′-dimethoxytrityl (DMT) protected hydroxyl is replaced with amonomethoxytrityl (MMT)-protected amine that can react with thecarboxylic acid of a PNA after deprotection. For PNA, the protectedN-terminal nitrogen is replaced with a DMT-protected hydroxyl that canreact with the phosphoramidite group on DNA after deprotection. Theseapproaches are more described in E. Uhlmann, et al., Angew. Chem. (Int'led.) 37: 2796-823 (1998), for example.

All of these modifications, whether used individually or in conjunctionwith one another, can affect the thermodynamic conditions of specificinteractions in an arbitrary nucleic acid network such that the bindingof desired strands or complexes is favored over clashing interactionswithout altering sequence content. All of these interactions can applyto any branch-mediated migration reaction, whether they are 3-way branchmigrations, such as solid-phase sequestering, toe-hold sequestering, ortoe-hold exchange, or are branch migrations that take place by othermechanisms, e.g., four-way branch migration, four-way accelerated branchmigration, or multi-strand complex migration.

In accordance with some embodiments, the kinetics of the chemicallymodified molecules for improved branch migration reaction can be tested.One approach is to measure the improvement that different modificationsprovide in accelerating or retarding the branch migration reactionversus a natural polynucleotide using a fluorescence kinetics assay (seeFIG. 8, for example). Here, the translator structure has a quencher onone strand and a fluorophore on the other. In the absence of thedisplacement strand, the fluorescence of the fluorophore is quenched,providing a baseline for the reaction. When the displacement molecule,which could be modified in the toe-hold and/or non-toe-hold regions, isadded to the translator, it will displace the strand with the quencherand in doing so produce a fluorescent signal. Therefore, the rate offluorescence “turn-on” in the system indicates the kinetics of thedisplacement reaction. This assay can be made more complex by requiringa larger circuit to evaluate before a final, fluorescence-producingdisplacement reaction or clashing strands could be added to compete withthe displacement strand for the toe-hold.

The approaches in accordance with the invention also can apply to anymolecules, natural or artificial, that are suitable for propagatinginformation, so long as a first molecule and a second molecule areinvolved, with the latter configured to bind with the former. At leastone of the first and second molecules, respectively, has a chemicalmodification relative to a reference molecule that has the same sequencecontent as the first molecule or the second molecule, as the case maybe. The modification causes the binding to have a free energy differentfrom that of a reference binding between the reference molecule and thefirst or second molecule, such that at least one of the following isrealized in the system: a probability of a productive binding is raised;or a probability of an unproductive binding is reduced.

Pursuant to the invention, as indicated above, a multistep process couldbe employed to achieve an improved nucleic acid network. This wouldentail examining the full network of nucleic acid translators underconsideration, including any clashing interactions, and then identifyingthe stretches of sequence that need to be modified in order best tofacilitate displacement events and to minimize clashing.

With respect to any given strand displacement reaction, thesemodifications could be made on the desired displacement molecule, on theclashing molecule, or on both. This is so because, for any translator orlogic gate with an available toe-hold, there will be a competitionbetween the desired displacement molecule and any clashing molecule tobind the toe-hold. Furthermore, increasing the ability of thedisplacement molecule to bind the toe-hold relative to the clashingmolecule will increase the rate at which the displacement reaction takesplace. Thus, increasing the ability of the displacement molecule to bind(lowering ΔG of binding) or decreasing the ability of the clashingmolecule(s) to bind (raising ΔG of binding) will have the effect ofincreasing the rate of the reaction. Since both of these changes in ΔGcan be accomplished via chemical modifications, pursuant to theinvention, it is important when considering which stretches of sequenceto modify that one should explore the possibility of modifying thedisplacement molecule alone, the clashing molecule alone, and both ofthese together.

According to embodiments of the invention, two parameters that could bevaried in this analysis are (i) the rate constants for the interactionbetween any two oligonucleotides and (ii) the length of the toe-holdsfor all of the oligonucleotides in the network. The former parameterwould be dictated by the chemical composition of the oligonucleotide andthe ΔG of its interactions with other oligonucleotides. The latterparameter would be the number of nucleotides in the toe-hold region ofsequence under consideration.

The kinetic rate constants needed to model a nucleic acid network couldbe calculated from the ΔG of hybridization between any twooligonucleotides. For the natural bases and many of the modifications,these values, which come from nearest-neighbor parameters, have beenreported in the literature. If they are not known already, they can beexperimentally determined through Van't Hoff analysis of meltingtemperature data, differential scanning calorimetry, or isothermaltitration calorimetry. Each of these methods would yield thethermodynamic parameters for the nucleic acid interaction in question,which then can be used to determine the ΔG of the reaction at anytemperature. The ΔG value then would be used to determine theequilibrium constant (K_(eq)) of the interaction. The equilibriumconstant would be proportional to the ratio of rate constants; hence,one could use known constants to solve for the necessary kinetic rateconstant for a given reaction.

Thus, the full set of rate constants would be obtained for themodifications under consideration for use in a nucleic acid logicnetwork, along with the lengths for all of the toe-holds. With thisinformation the system could be modeled to determine the time coursebehavior of the network, and also to determine where specificmodifications could be employed to optimize the productive displacementreactions relative to clashing interactions. Additionally, the length ofspecific toe-hold regions could be varied in the model. The networkwould be optimized by varying modifications at specific locations and bysimulating the reactions in the network with different length toe-holds.These calculations would be employed to determine the optimalmodification and toe-hold length for each component that produces themost favorable time course behavior of the network.

The network also could be optimized by experimentally changing themodifications and toe-hold lengths and then studying the time coursebehavior in the laboratory, as opposed to simulating the behavior with amathematical model.

Given a fully optimized network, the necessary oligonucleotides could besynthesized with standard phosphoramidite chemistry or with theapproach(es) reported in the literature for specific modifications. Anytranslator or gate structure that consists of more than oneoligonucleotide could be constructed by mixing the individualoligonucleotides together and then annealing them, first by heating themixture to above the melting temperature of all possible duplexes andthen slowly cooling it. This would cause the oligonucleotides tohybridize, forming the most stable structure that the particular set ofnucleic acid sequences can adopt. These structures then could bepurified before they were used in the network. Once all of thetranslators, gates, and other components are designed, synthesized, andannealed, the network could be applied to the target assay, diagnostic,or biological system.

While particular embodiments of the subject invention have beendiscussed, they are illustrative only and not restrictive of theinvention. A review of this specification will make many variations ofthe invention apparent to those skilled in the field of the invention.The full scope of the invention should be determined by reference bothto the claims below, along with their full range of equivalents, and tothe specification, with such variations.

CITED PUBLICATIONS

The following publications may aid understanding or practicingembodiments of the invention. Each cited publication is incorporated byreference in its entirety.

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What is claimed is:
 1. A method for preparing an improved nucleicacid-based molecular computing system, comprising: (1) identifying anucleic acid-based computing system that comprises (i) an input nucleicacid strand comprising a first fragment (A) and a second fragment (B);(ii) a target, incompletely base-paired nucleic acid duplex comprising afirst strand and a second strand, wherein the first strand comprises afirst fragment (B′) and a second fragment (A′), the second strandcomprises a first fragment (B) and a second fragment (C), and the targetduplex comprises a duplex region formed by base-pairing between B and B′and two single-stranded regions, A′ and C, and wherein the input strandcan bind with the first strand of the target duplex under hybridizingconditions to invoke a strand displacement reaction to produce an outputduplex formed between the input strand (A-B) and the first strand of thetarget duplex (B′-A′), and (iii) a clashing, incompletely base-pairednucleic acid duplex comprising a first strand and a second strand,wherein the first strand comprises a first fragment (C′) and a secondfragment (B′), the second strand comprises a first fragment (C) and asecond fragment (D), and the clashing duplex comprises a duplex regionformed by base-pairing between C and C′ and two single-stranded regionsB′ and D, wherein the second strand of the target duplex can bind withthe first strand of the clashing duplex under hybridizing conditions toinvoke a strand displacement reaction to produce an output duplex formedbetween the second strand of the target duplex (B-C) and the firststrand of the clashing duplex (C′-B′), and wherein the second fragment(B) of the input strand can bind with the single-stranded region B′ ofthe clashing duplex under hybridizing conditions; and then (2)synthesizing, in an aqueous solution, a variant of said nucleicacid-based molecular computing system that differs from the latter by(i) an incorporation into the first fragment (B) of the second strand ofthe target duplex a first chemical modification that causes binding withthe second fragment (B′) of the first strand of the clashing duplex tohave a decreased hybridization free energy, and/or (ii) an incorporationinto the second fragment (B) of the input strand a second chemicalmodification that causes binding with the second fragment (B′) of thefirst strand of the clashing duplex to have an increased hybridizationfree energy, such that the first fragment (B) of the second strand ofthe target duplex, as compared to the second fragment (B) of the inputstrand, binds to the second fragment (B′) of the first strand of theclashing duplex to form a more stable duplex region, whereby the variantis improved over the nucleic acid-based molecular computing system interms of a reduced incidence of hybridization between the input strandand the clashing duplex.
 2. The method of claim 1, wherein the variantcomprises the first chemical modification.
 3. The method of claim 1,wherein the variant comprises the second chemical modification.
 4. Themethod of claim 1, wherein the input strand, the target duplex, and theclashing duplex form part of an enzyme-free, nucleic acid logic gateselected from the group consisting of an AND gate, a NOT gate, an ORgate, a NAND gate, a NOR gate, an XOR gate, and an XNOR gate.
 5. Themethod of claim 1, wherein the first or second chemical modification isselected from the group consisting of (i) replacing thesugar-phosphodiester backbone of said nucleosides with a pseudo-peptidebackbone, (ii) modifying the sugar moiety of said nucleosides, and (iii)substituting an analogue for the nitrogenous base of at least one ofsaid nucleosides.
 6. The method of claim 5, wherein the first or secondchemical modification comprises replacing the sugar-phosphodiesterbackbone of said nucleosides with a pseudo-peptide backbone into which aguanidinium functional group is incorporated.
 7. The method of claim 5,wherein the first or second chemical modification comprises substitutinga tricyclic cytosine analogue for the nitrogenous base of at least oneof said nucleosides.
 8. The method of claim 5, wherein the first orsecond chemical modification comprises introducing a heteroatom at the2′-position of said sugar moiety.
 9. The method of claim 1, wherein thestrand displacement reaction comprises a toe-hold-mediated stranddisplacement.